Abstract
This paper is mainly concerned with the true interval of orthogonality for a sequence of orthogonal polynomials, which is the smallest closed interval containing the limit points of the set of zeros of the polynomials. We give bounds for the endpoints of this interval in terms of the coefficients in the three term recurrence formula and show them to be generalizations of most existing results. Similar findings are reported for the limit interval of orthogonality, which is defined as the smallest closed interval containing the derived set of the set of limit points. Our bounds are based upon an oscillation theorem for orthogonal polynomials which is of independent interest.
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